Question: Solve for $x$ and $y$ using substitution. ${-2x-3y = 11}$ ${y = 6x+3}$
Solution: Since $y$ has already been solved for, substitute $6x+3$ for $y$ in the first equation. ${-2x - 3}{(6x+3)}{= 11}$ Simplify and solve for $x$ $-2x-18x - 9 = 11$ $-20x-9 = 11$ $-20x-9{+9} = 11{+9}$ $-20x = 20$ $\dfrac{-20x}{{-20}} = \dfrac{20}{{-20}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = 6x+3}\thinspace$ to find $y$ ${y = 6}{(-1)}{ + 3}$ $y = -6 + 3$ $y = -3$ You can also plug ${x = -1}$ into $\thinspace {-2x-3y = 11}\thinspace$ and get the same answer for $y$ : ${-2}{(-1)}{ - 3y = 11}$ ${y = -3}$